Uniform Circular Motion Problem. Help

Then, use this relationship to solve for the speed in the vertical case.In summary, to determine the speed of the stone in the vertical case, we can use the relationship between speed, string length, and tension that was found in the horizontal case. Using this relationship and the given information about the tension in the vertical case, we can solve for the speed of the stone.
  • #1
aki_23
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0

Homework Statement


A stone tied to a string with length 1.10 m is whirled in a circle both horizontally and vertically with the same constant speed. In the vertical case the maximum tension in the string is 15.0% larger than the tension that exists when the string was horizontal. Determine the speed of the stone.

Homework Equations


a = v2/r

The Attempt at a Solution


for horizontal, my equation was Fc = mv2/r

for vertical, my equation was Fc = Ft - mg, because at the bottom of the vertical circle fg is present
mv2/r = 0.15Ft - mg

I don't know how to take this further
 
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  • #2
Consider the horizontal case in more detail. There are vertical forces too. You should be able to find a relationship between the speed, the string length, and the tension.
 

1. What is uniform circular motion?

Uniform circular motion is the motion of an object traveling in a circular path at a constant speed. This means that the object is moving at the same speed and direction at all points along the path.

2. How is uniform circular motion different from regular circular motion?

Uniform circular motion is a type of circular motion where the speed of the object remains constant, while regular circular motion can have varying speeds. In uniform circular motion, the object is also constantly changing direction, while in regular circular motion, the object may only change direction at certain points along the path.

3. What is the role of centripetal force in uniform circular motion?

Centripetal force is the force that keeps an object moving in a circular path. In uniform circular motion, the centripetal force is always directed towards the center of the circle and is responsible for constantly changing the direction of the object's velocity.

4. How is the period of uniform circular motion related to the speed and radius of the object?

The period of uniform circular motion is the time it takes for an object to complete one full revolution around the circle. It is directly proportional to the radius of the circle and inversely proportional to the speed of the object. This means that as the radius increases, the period also increases, while as the speed increases, the period decreases.

5. What is the equation for calculating the centripetal acceleration in uniform circular motion?

The centripetal acceleration can be calculated using the equation a = v^2 / r, where a is the centripetal acceleration, v is the speed of the object, and r is the radius of the circle. This equation shows that the centripetal acceleration is directly proportional to the square of the speed and inversely proportional to the radius.

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